The villa owner with a weekend 4x4: desert recovery is a different trade
Getting stuck at Al Qudra, Al Badayer or Sweihan is not a towing job and it is a waste of money to book one. A city flatbed cannot leave tarmac; the driver will look at the sand, photograph your car from the road and leave. Desert recovery is done by someone in a capable 4x4 with a winch, kinetic rope, rated shackles, boards and, more important than any of it, sand judgement. The price reflects the drive out, the risk to their own vehicle and the skill: a straightforward pull-out near an access road might sit at AED 300-600, while a deep bog-down far off the track, at night, can go beyond any standard range and is quoted case by case.
What you do before the recovery arrives decides how easy it is. Stop digging the moment the wheels spin freely; every further attempt buries the chassis deeper. Drop tyre pressures hard if you have not already. Note a precise location, a dropped pin from your phone's map app is the single most useful thing you can send, along with which track or gate you entered from and a photo showing how deep the car sits. Stay with the vehicle. A car is visible from a distance in open desert; a person walking out in summer heat is in far more danger than a person waiting in shade beside a stuck car.